Related papers: Quantization of pseudo-differential operators on t…
We consider toroidal pseudodifferential operators with operator-valued symbols, their mapping properties and the generation of analytic semigroups on vector-valued Besov and Sobolev spaces. We show that a parabolic toroiodal…
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…
We prove a general black box result which produces algebras of pseudodifferential operators (ps.d.o.s) on noncompact manifolds, together with a precise principal symbol calculus. Our construction (which also applies in parameter-dependent…
The notion of pseudo-differential operators with coefficients in a continuous trace algebra over a manifold are introduced and their index theory is studied. The algebra of principal symbols in this calculus provides an abstract Poincar\'e…
We introduce two new classes of pseudo-differential operators on open curves. They correspond via a change of variables to subclasses of the periodic pseudo-differential operators, which respectively stabilize even and odd functions. The…
We study a class of pseudo-differential operators with oscillating symbols or osc illating amplitudes appearing in the long-range scattering theory. We develop the basic calc ulus for operators from such classes and solve some concrete…
In this monograph we develop magnetic pseudodifferential theory for operator-valued and equivariant operator-valued functions and distributions from first principles. These have found plentiful applications in mathematical physics,…
In this paper, we introduce a parametric pseudodifferential calculus on noncommutative $n$-tori which is a natural nest for resolvents of elliptic pseudodifferential operators. Unlike in some previous approaches to parametric…
In this paper, we present first results of our investigation regarding symbolic pseudo-differential calculi on nilpotent Lie groups. On any graded Lie group, we define classes of symbols using difference operators. The operators are…
In this paper, we study the boundedness of pseudodifferential operators with symbols in the H\"ormander class $S^0_{\rho,\rho}$ on $\alpha$-modulation spaces $M_{p,q}^{s,\alpha}$, and consider the relation between $\alpha$ and $\rho$. In…
We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…
A symbolic calculus for a pseudo-differential operators acting on sections of a homogeneous vector bundle over a compact homogeneous space $G/H$ with compact $G$ and $H$ is developed. We realize the symbol of a pseudo-differential operator…
We give a complete characterization of the continuity of pseudodifferential operators with symbols in modulation spaces $M^{p,q}$, acting on a given Lebesgue space $L^r$. Namely, we find the full range of triples $(p,q,r)$, for which such a…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols…
In this work we obtain sharp $L^p$-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis…
We aim at extending the definition of the Weyl calculus to an infinite dimensional setting, by replacing the phase space $ \mathbb{R}^{2n}$ by $B^2$, where $(i,H,B)$ is an abstract Wiener space. A first approach is to generalize the…
We show the existence of fundamental solutions for p-adic pseudo-differential operators with polynomial symbols.
We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann zeta-function and the related Dirichlet…
In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ T}\times \mathbb{Z})$ (associated to a suitable weight function $\Lambda$ on…